One way to avoid that is to find her before you start and put the frame that she is on into an empty box with an inner cover underneath it so that she won’t fall out of the box.
I don’t have a Flow hive 2, but the the screen is designed to let wax and SHB fall through, so mites certainly will - they are tiny (only around 1mm across)!
You only need a sticky board if you don’t have a hive with a slider. So you shouldn’t need one.
It depends on exactly how you do it. If you just count a clean slider every 24 hours, that is horribly inaccurate. However, if you have an oxalic acid vaporizer and you do an “accelerated mite drop count”, that is very accurate. Here is how you do it:
I photograph the slider when I pull it out, so that I can count at leisure, plus I have a record of the count. If you have a good camera, bright lighting and a steady hand, the photo is really helpful.
If you can’t do that, you really need powdered sugar or alcohol. 